Finite element vibration analysis of composite beams based on higher-order beam theory

Abstract

This paper presents a new finite element formulation for the free vibration analysis of composite beams based on the third-order beam theory. This work also studies the influence of the mass components resulting from higher-order displacements on the frequencies of flexural vibration. By using Hamilton's principle, the variational consistent equation of motion in matrix form corresponding to the third-order shear deformation theory is derived. The resulting mass matrices are decomposed into three parts, i.e., the usual part, including the rotary inertia, corresponding to first-order theory, the part resulting from higher-order displacement, and the part resulting from the coupling between the different components of the axial displacement. The numerical examples show that the higher-order and coupling mass matrices have a significant influence on the frequencies of high mode flexural vibration. The present element formulation for composite beams can be easily extended to composite plates and shells. © 1999 Academic Press.